1. Field of the Invention
The present invention relates to a method of generating sine/cosine function and an apparatus using the same in digital signal processor, and more particularly to a method for generating sine/cosine function values corresponding to phase values of first to fourth quadrants by utilizing a look-up table having one of sine and cosine function values corresponding to phase values of any one quadrant, and an apparatus using the same.
2. Description of the Prior Art
Generally, in digital communication system, a phase error (.theta.) is generated when phases of a carrier signal between a transmitting side and a receiving side are not synchronized during a transmission of a complex symbol. At this time, the transmitted complex symbol is multiplied by e.sup.j.theta., affecting demodulated complex symbols. As a result, the demodulated complex symbol rotates in a complex plane as much as the phase error (.theta.). Due to this rotation, the demodulated complex symbol is moved to the detection area of other symbols in a constellation, and an error is generated during symbol detection process. Therefore, a reliable decoding depends on an accurate phase synchronization, and for this purpose, a carrier recovery circuit in receiver is utilized.
The carrier recovery circuit comprises a phase locked loop (PLL). The PLL comprises a phase error detector, a loop filter, and a trigonometric function look-up table. Here, the phase error detector detects a phase error from the phase component of a pure carrier signal, in which the phase component generated by the modulation process is removed from a received signal. The phase error (.theta.) with removed high frequency band component by the loop filter is applied to the trigonometric function look-up table to generate a phase-corrected signal (cos .theta.-jsin .theta.), and the original carrier signal is recovered by complex multiplying the phase-corrected signal (cos .theta.-jsin .theta.) by the received signal.
The sine and cosine function values necessary for generating the phase-corrected signal (cos .theta.-jsin .theta.) are stored in the look-up table. These function values are obtained faster by utilizing the look-up table than a circuit for directly calculating them, hence it is widely used in various related fields.
FIG. 1 shows an input/output relation of a conventional trigonometric function look-up table used for the above described process. Referring to FIG. 1, a first phase signal (.theta.') is divided by 2.pi. in a 2.pi. modulo operator 11, and the remainder value is outputted as a second phase signal (.theta.). A sine look-up table 12 and a cosine look-up table 13 output respectively sine function values (sin .theta.) and cosine function values (.theta.) stored in a location addressed by the second phase signal (.theta.).
Meanwhile, when the sine and cosine look-up tables 12 and 13 illustrated in FIG. 1 are stored in a read-only-memory (ROM), they have a memory map as illustrated in FIG. 2. For example, the sine look-up table 12 stores 2.sup.n number of the function value for phase signals of n-bits in the range of 0 to 2.pi..
Accordingly, separate look-up tables are required to generate sine and cosine function values, respectively. Consequently, 2.sup.n number of storage location is required when the phase signal (.theta.) is composed of n-bits, and at least 2.sup.n .times.M bits storage capacity is required for each look-up table when the function values are composed of M-bits. In this case, the conventional look-up table has a problem in that the higher the accuracy for the function value, the look-up table capacity increases.